The Merseyside club commented after the Daily Star Sunday report the Italian striker filmed himself at a party in his apartment, and the club has "strongly expressed its disappointment to the player".
In a statement, Everton said they were "appalled to learn of an incident in which a first-team player ignored government guidance and club policy in relation to the coronavirus crisis".
The club added: "Everton has regularly stressed the importance of following all the government guidelines - including rules and advice for inside and outside of the home - through a series of official communications to all staff members, including players.
"The amazing people in the NHS deserve the utmost respect for their hard work and sacrifice.
"The best way to show them respect is by doing everything we can to protect them."
The 20-year-old striker made a £25.1 million summer switch to Everton from Juventus, but scored just one goal in 22 first team appearances.
He was dropped from the squad for a game against Southampton in November by then-manager Marco Silva.
This was a disciplinary measure after Moise was late for a team meeting for the second time.